{"categories":[],"blog_url":"https://autotaker.hatenablog.com/","image_url":null,"author_name":"autotaker","published":"2017-11-11 14:30:03","url":"https://autotaker.hatenablog.com/entry/2017/11/11/143003","width":"100%","html":"<iframe src=\"https://hatenablog-parts.com/embed?url=https%3A%2F%2Fautotaker.hatenablog.com%2Fentry%2F2017%2F11%2F11%2F143003\" title=\"Code Blue CTF Writeup - autotaker&#39;s blog\" class=\"embed-card embed-blogcard\" scrolling=\"no\" frameborder=\"0\" style=\"display: block; width: 100%; height: 190px; max-width: 500px; margin: 10px 0px;\"></iframe>","type":"rich","author_url":"https://blog.hatena.ne.jp/autotaker/","version":"1.0","title":"Code Blue CTF Writeup","provider_name":"Hatena Blog","height":"190","provider_url":"https://hatena.blog","description":"Common Modulus 1-3 \u3044\u305a\u308c\u3082RSA\u3092\u89e3\u8aad\u3059\u308b\u554f\u984c\u3002 \\(C_1 = M^{e_1} \\mod N\\) \\(C_2 = M^{e_2} \\mod N\\) \u304c\u4e0e\u3048\u3089\u308c\u308b\u3002Common Modulus 1\u3067\u306f\\(e_1, e_2\\)\u306f\u4e92\u3044\u306b\u7d20\u306a\u306e\u3067\u3001\u62e1\u5f35\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u306e\u4e92\u9664\u6cd5\u306b\u3088\u308a \\[ x e_1 + y e_2 = 1 \\] \u3068\u306a\u308b\\(x, y\\)\u304c\u6c42\u3081\u3089\u308c\u308b\u3002\u3059\u308b\u3068 \\[ C_1^x C_2^y = M^{x e_1 + y e_2} = M^1 = M \\] \u3068\u306a\u308b\u306e\u3067\u5fa9\u53f7\u3067\u304d\u308b\u3002Common Modulus 2\u3067\u306f\\(\\mathrm{gcd}(e_1, e_2) = 3\\)\u2026","blog_title":"autotaker's blog"}